She sounds manipulative. It is not right of someone to hold another hostage by emotional threats, tell her if she is serious you will call 911 for assistance or take her to a hospital. Do not allow her to continue trying to hold you responsible for her feelings.

I've been suicidal before but I've never and no one should be using suicide to manipulate another person. If it were me I would call 911 and tell them what she is doing and tell them you are concerned she will follow though if she doesn't get what she wants( a relationship with you) and let them deal with her. Tell her you will no longer listen or talk to her if she is going to threaten you.